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Signatures of stellar surface structure
Dainis Dravins - Lund Observatory
www.astro.lu.se/~dainis
Stellar atmosphere theory classics…
Unsöld (1938, 1968); Mihalas (1969, 1978)
Some essential steps in
model-atmosphere analysis
for determining stellar abundances
(Bengt Gustafsson)
ASSUMPTIONS FOR THE RADIATIVE PART OF STELLAR MODEL ATMOSPHERES
TE Thermodynamic
Equilibrium
LTE Local Thermodynamic
Equilibrium
KE Kinetic Equilibrium
One single temperature T determines
all properties of gas and radiation
One local temperature in each spatial
point determines:
One local temperature in each spatial
point determines:
Source function = Planck function
Electron velocities:
Maxwell-Boltzmann distribution
Excitation: Boltzmann equation
Excitation: For each energy level:
statistical equilibrium between exciting
& de-exciting processes
Ionization: Saha equation
Ionization: Statistical equilibrium
between ionizing & recombining
processes
Radiation field: Isotropic, given by
the Planck function
Radiation field: Equation of radiative
transfer (depends on conditions along
the photon mean-free-path)
Radiation field: Equation of radiative
transfer, coupled to equilibrium
equations for excitation & ionization
Information needed: No further
knowledge needed (and none more
can be obtained)
Information needed: Local values for
kinetic temperature. Chemical
composition and laboratory data for
opacities of various elements as
function of pressure, temperature, and
wavelength
Information needed: As for LTE, plus
data for atomic processes such as
photoexcitation cross sections;
collisional [de]excitation & ionization;
spontaneous & stimulated emission,
free-free emission & absorption;
radiative & dielectronic recombination,
for different species, for different
electron energies, as function of
wavelength, etc.
G.Worrall & A.M.Wilson: Can Astrophysical Abundances be Taken Seriously?, Nature 236, 15
Deduced quiet-Sun
temperature
distribution
Approximate depths
where various
continua and lines
originate are marked
J.E.Vernazza, E.H.Avrett,
R.Loeser: Structure of the
solar chromosphere. III Models of the EUV brightness
components of the quiet-sun
ApJS 45, 635
Paradigms of stellar atmosphere analyses
Craig & Brown (1986)
But…
SYNTHETIC LINE PROFILES & SHIFTS
1-D models disagree with observations
(data from solar flux atlas)
M.Asplund, Å.Nordlund, R.Trampedach, C.Allende Prieto, R.F.Stein: Line formation in solar granulation.
I. Fe line shapes, shifts and asymmetries, Astron.Astrophys. 359, 729
ASSUMPTIONS FOR THE DYNAMIC PART OF STELLAR MODEL ATMOSPHERES
Classical model atmosphere
Hydrodynamic simulations
Vertical structure of temperature and pressure from
assumed convective heat exchange over a mixing-length.
Pressure follows from gas density and temperature
Vertical structure of temperature and pressure from
time-dependent 3-dimensional hydrodynamic simulations,
coupled to radiative transfer. Pressure now also includes
contributions from turbulence and shock waves
Atmosphere horizontally homogenous,
also no time variability
Atmosphere horizontally inhomogenous, parameters
depend on lateral position, and also evolve with time
Spectral line broadening: Assumed [often isotropic]
“macroturbulence”
Spectral-line broadening: Largely follows from the
calculated RMS velocity amplitudes
Spectral-line strengths: Assumed [often isotropic]
“microturbulence”
Spectral-line strengths: Largely follow from calculated
velocity and temperature gradients
Spectral-line shapes & shifts: Not modeled
Spectral-line shapes & shifts: Arising from correlations
between velocity, temperature, and local line strength
Comparison to observations: Model parameters
adjusted ad hoc to agree with observations
Comparison to observations: No adjustable physical
parameters. Temporally and spatially averaged simulation
sequences predict various stellar properties. If do not
agree with observations, the physical, mathematical and
numerical model approximations have to be adjusted
Real line
formation
OBSERVED SOLAR GRANULATION
Dutch Open Telescope (La Palma)
SIMULATED SOLAR GRANULATION
Hans-Günter Ludwig (Lund)
“Wiggly”
spectral lines
of solar
granulation
“Wiggly" spectral lines in
the solar photosphere
inside and outside a region
of activity, reflecting
rising and sinking motions in
granulation (wavelength
increases to the right).
The central part crosses a
magnetically active region
with reduced velocity
amplitudes. (W.Mattig)
Spatially resolved line profiles of the Fe I 608.27 nm line (exc = 2.22 eV) in a 3-D solar simulation.
The thick red line denotes the spatially averaged profile.
The steeper temperature structures in upflows tend to make lines stronger (blue-shifted components).
M.Asplund: New Light on Stellar Abundance Analyses: Departures from LTE and Homogeneity, Ann.Rev.Astron.Astrophys. 43, 481
Spatially
resolved
line profiles
& bisectors
of solar
granulation
(modeled)
M.Asplund, Å.Nordlund,
R.Trampedach,
C.Allende Prieto, R.F.Stein:
Line Formation in Solar
Granulation. I.
Fe Line Shapes, Shifts and
Asymmetries,
Astron.Astrophys. 359, 729
SYNTHETIC LINE PROFILES & SHIFTS
Good agreement for solar-type stars in 3-D
(no micro-, nor macroturbulence)
M.Asplund, Å.Nordlund, R.Trampedach, C.Allende Prieto, R.F.Stein: Line formation in solar granulation.
I. Fe line shapes, shifts and asymmetries, Astron.Astrophys. 359, 729
CHANGING STELLAR PARADIGMS
 RECENT PAST: ”Inversion” of line profiles; “any part of a
profile corresponds to some height of formation”
 Adjustable parameters, e.g., ”micro-” & ”macro-turbulence”
 NOW: Stellar line profiles reflect statistical distribution
of lateral inhomogeneities across stellar surfaces
 Not possible, not even in principle, to ”invert” observed
profiles into exact atmospheric parameters
 Confrontation with theory through ”forward modeling”:
numerical simulations of radiation-coupled stellar
hydrodynamics, and computation of observables
BISECTORS & SHIFTS: Line-strength
Fe I 680.4
Fe I 627.1
Fe I 624.0 nm
Predicted (solid) and observed bisectors for differently strong solar lines; 3-D hydrodynamic modeling on an
absolute velocity scale. (Classical 1D models produce vertical bisectors at zero absolute velocity.)
M.Asplund, Å.Nordlund, R.Trampedach, C.Allende Prieto, R.F.Stein: Line formation in solar granulation.
I. Fe line shapes, shifts and asymmetries, Astron.Astrophys. 359, 729
STELLAR CONVECTION
Matthias Steffen (Potsdam) & Bernd Freytag (Uppsala)
Solar
granulation
at different
depths
3-D models show change of
flow topology with depth z
(positive into the Sun).
The surface pattern
consisting of lanes
surrounding granules
changes into a pattern of
disconnected downdrafts.
R.F.Stein & Å.Nordlund:
Topology of convection beneath
the solar surface ,
Astrophys.J. 342, L95 &
H.C.Spruit, Å.Nordlund,
A.M.Title: Solar Convection,
ARAA 28, 263
Solar granulation at 200 nm
3D radiation hydrodynamics simulation of solar surface convection
M.Steffen & S.Wedemeyer
Quiet solar granulation at 200 nm
Quiet solar granulation at 445 nm
Effects of
magnetic fields
MAGNETIC & NON-MAGNETIC GRANULATION
Difference in solar granulation between magnetic and non-magnetic regions. Continuum images of the
same area, blackened out (left) where the average field strength is less than 75 G, and (right) where
the field strength is larger than 75 G. (Swedish Vacuum Solar Telescope, La Palma)
H.C.Spruit, Å.Nordlund, A.M.Title: Solar Convection, Ann.Rev.Astron.Astrophys. 28, 263 (1990)
MAGNETIC & NON-MAGNETIC BISECTORS
Line bisectors gradually closer to an active region (dashed), compared to that of the quiet Sun.
Positions relative to the Ca II K plage are indicated.
F.Cavallini, G.Ceppatelli, A.Righini, Astron.Astrophys. 143, 116
UNDERSTANDING STELLAR SURFACES
theory and observations interact about...
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Spectral-line strengths
Spectral-line widths
Line-profile shapes
Line asymmetries and bisector patterns
Time variability in irradiance and spectrum
Stellar surface imaging
Relative & absolute wavelength shifts
PROGRESS IN SCIENCE
is driven by ...
 Confrontation between theory and observation
 Falsification of theoretical hypotheses
 New observational measures requiring explanation
PROGRESS IN SCIENCE
is not driven by ...
Agreement between theory and observation
(when they agree, not much new can be learned)
PROGRESS IN STELLAR PHYSICS
Requires disagreement between
theory and observation !
Different stars
Fe I-line
bisectors
in Sun and
Procyon
(F5 IV-V)
[observed]
C.Allende Prieto, M.Asplund, R.J.García López, D.L.Lambert: Signatures of Convection in the Spectrum of Procyon:
Fundamental Parameters and Iron Abundance, Astrophys.J. 567, 544
Average bisectors for theoretical Fe I lines produced in the time-dependent hydrodynamical three-dimensional model atmosphere for lines of
different strength.
Signatures of Convection in the Spectrum of Procyon: Fundamental Parameters and Iron Abundance
C.Allende Prieto, M.Asplund, R.J.García López, D.L.Lambert
Astrophys.J. 567, 544 (2002)
Hydrodynamic models: emperature and pressure distributions in a model of Procyon (Martin Asplund)
A-TYPE STELLAR CONVECTION
Bernd Freytag (Uppsala) & Matthias Steffen (Potsdam)
Hydrodynamic models: Temperature distributions in the Sun, and in a metal-poor star.
Surface layers are much cooler in 3-D than in 1-D; expansion cooling dominates over radiative
heating (effect of lines opposite to that in 1-D models). The zero-point in height corresponds to
average continuum optical depth unity. Dashed: 1D hydrostatic model.
STELLAR CONVECTION – White dwarf vs. Red giant
Snapshots of emergent intensity during granular evolution on a 12,000 K white dwarf (left)
and a 3,800 K red giant. Horizontal areas differ by dozen orders of magnitude: 7x7 km2
for the white dwarf, and 23x23 RSun2 for the giant. (Ludwig 2006)
Cool supergiant (”Betelgeuse”)
Bernd Freytag (Uppsala)
Stellar
astrometric
“flickering”
Two situations during
granular evolution: At left
a time when bright [red]
elements are few, and
the star is darker than
average; At right, many
bright elements make the
star brighter.
Spatial imbalance of
brighter and darker
patches displace the
photocenter [green dot]
relative to the geometric
center [blue dot].
(Ludwig 2006)
Limits to
information content
of stellar spectra ?
“ULTIMATE” INFORMATION CONTENT OF STELLAR SPECTRA ?
3-D models predict detailed line shapes and shifts
… but …
their predictions may not be verifiable due to:
 Uncertain laboratory wavelengths
 Absence of relevant stellar lines
 Blends with stellar or telluric lines
 Data noisy, low resolution, poor wavelengths
 Line-broadening: rotation, oscillations
Absorption in the
Earth’s atmosphere
Wavelength noise
MODELING SPECTRA (not only single lines)
LTE solar 3-D spectra, assuming [O]=8.86 for two different van der Waals damping constant (black lines).
Blue line: observed disk center FTS spectrum by Neckel (“Hamburg photosphere”), slightly blueshifted.
Hans-Günter Ludwig (2006)
O I LINE PROFILES & SHIFTS
O I 777.19
 777.41
 777.53
LTE solar 3-D hydrodynamic spectra, assuming [O]=8.86, for two different damping constants (black lines).
Blue line: observed disk center FTS spectrum, slightly blueshifted.
Hans-Günter Ludwig (2006)
Limits from wavelength noise ?
Bisectors of 54 Ti II lines at solar disk center from Jungfraujoch Atlas (grating
spectrometer; left); and as recorded with the Kitt Peak FTS . Bisectors have similar
shapes but differ in average lineshift, and scatter about their average.
Chromosphere &
radio observations
Solar Optical Telescope (SOT) on Hinode/Solar-B
Corona
Chromosphrer
Temperature
minimum
Photosphere
Magnetic
field
Solar Optical Telescope on board HINODE (Solar-B)
G-band (430nm) & Ca II H (397nm) movies
A view at the solar chromosphere with ALMA
3-D radiation hydrodynamics simulation of the non-magnetic solar atmosphere
M.Steffen, H.-G.Ludwig, S.Wedemeyer, H.Holweger, B.Freytag
Monochromatic image at 0.35 mm
Monochromatic image at 3 mm
Spatially resolved
stellar spectroscopy
Solar granulation near the limb (upward on the image)
Filtergram at 488 nm; Swedish 1-m Solar Telescope on La Palma (G.Scharmer & M.G.Löfdahl)
Center-toLimb
Variation
Åke Nordlund
(Copenhagen)
Center-to-limb changes of solar spectral lines
Spatially and temporally averaged Fe I 608.2
profiles and bisectors at different viewing
angles (center-to-limb distances).
Continuum intensity is normalized to that at
disk center.
Thick solid lines represent disk-center.
Note the "limb effect": smaller blue-shift
toward the limb
M.Asplund, Å.Nordlund, R.Trampedach, C.Allende Prieto, R.F.Stein: Line formation in solar granulation.
I. Fe line shapes, shifts and asymmetries, Astron.Astrophys. 359, 729
Center-to-limb
line-profile
changes
in Procyon
Evolution of spatially averaged
line profiles and bisectors in
the Procyon model, leading to
the global averages.
Time variability increases
toward the limb, and the limb
effect has opposite sign from
that on the Sun.
D.Dravins & Å.Nordlund
Stellar Granulation IV.
Line Formation in
Inhomogeneous
Stellar Photospheres
A&A 228, 84
SPATIALLY RESOLVED STELLAR SPECTROSCOPY
Future observational challenges include...
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Center-to-limb changes of line profiles
Center-to-limb changes of line shifts
Center-to-limb changes of time variablity
Changes across stellar active regions
WORK STILL TO DO ...
…